First rule for making cool outfits for your space stage creature: don't be afraid to experiment. Get creative. Many parts can be used in non-conventional ways. On the creature above, for instance, I've used the Moon Gas Sensor for the arms and legs (it usually goes in the head). The boots were made with a hat and a chest plate.
Aqua View Masks make great neck braces. Try to make your creature with a thinner neck, and use the "Tab" key and arrow handlers to morph and position the part properly.
The Creepy & Cute Parts Pack has a bunch of very useful paint options and parts. If you're making a creature straight for the Space Stage, you can use the Mittenfist part as a gloved hand and the Footoon foot as a shoe.
More isn't always best. While you can use lots of parts for a detailed armor, you should check if the parts match each other aesthetically. There are several styles of outfit parts, and they don't always go well together. You can use instead a smart paint job for the illusion of a skin tight suit.
It doesn't have to be a humanoid creature to enjoy the comfort of a soft, warm suit. Though you may want to keep the base creature simple. If the creature has too many parts, it can be hard to tell if it's even wearing a suit.
All the creatures above can be found in my profile.